European Online Journal of Natural and Social Sciences 2015;
Vol.4, No.1 Special Issue on New Dimensions in Economics, Accounting and Management
ISSN 1805-3602
www.european-science.com
Production Function of the Mining Sector of Iran
1
Seyyed Ali Zeytoon Nejad Moosavian1*
Department of Economics, Poole College of Management, North Carolina State University,
Raleigh, North Carolina, USA;
*
E-mail: [email protected]
Abstract
The purpose of this study is to estimate the production function and the structure of
production in the mining sector. Several studies have been conducted in the field of estimating
production functions of various economic sectors; however, less attention has been paid to the
mining sector. By validating variables using augmented Dickey-Fuller and Phillips-Perron tests, this
study estimated the production function under different scenarios using co-integration method and
time series data for 1976-2006. The unconstrained Cobb-Douglas function in Tinbergen scenario
provided better results in accordance with theoretical foundations of economics, statistics and
econometrics. Results show that the structure of mining sector of Iran is capital-intensive and workintensive. Based on findings, the production elasticity of capital and labour are 0.44 and 0.41,
respectively. On the other hand, the coefficient of time variable, as an indicator of changes and
technological developments in production, is significant representing a positive effect of technical
changes on output of the mining sector.
Keywords: mine, production function, capital stock, employment, co-integration, productive
elasticity
Introduction
The mining sector is considered as one of the parent industries. In most cases, although it
owns a small share in GDP, its effect is considerably on wealth generation. High diversity and
abundance of mineral wealth has created a potential for Iranian economy. The mining sector is of
great importance in employment and balanced regional economic development. Iran is a rich
country in terms of mineral wealth; to use this rich potential for growth and economic development,
deserves a considerable thought(Zeytoonnejad, 2005).
Basically, the mining sector refers to that part of the economy which explores, exploits and
mineralizes. Based on this definition, measures and activities such as smelting, refining, rolling, etc.,
relate to the mineral industry and not mining sector. Accordingly, the following form can be defined
to justify the activities in the mining sector.
Figure 1: separation of activities of the mining sector and mineral industry
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Seyyed Ali Zeytoon Nejad Moosavian
With more than 55 billion tons of confirmed and probable mineral reserves of minerals, Iran
is one of the first 12 countries with mineral reserves. However, the mining sector is not in a good
place in the economic development of Iran. For many countries, such underground resources are an
opportunity for growth and economic development ;however, Iran could not use these opportunities
for some reason (Mining and Development, 2005). Lack of studies in regard to production in this
sector, perhaps, is one of the missing links in exploitation of opportunities in the mining sector. With
a broad perspective, Economics today analyses the problem of production bya technical relationship
called as production function.
This article is organized as follows .After the introduction, the research problems are
discussed. In the first section, the theoretical basis of the production function is checked. The second
section reviews some empirical studies in the field of estimated production function. In the third
section, the mining sector is analysed in the Iranian economy. In the fourth and fifth sections,
respectively, the model is determined and estimated. Finally, the last section summarizes the
conclusions. This article seeks to answer the following questions:
- What is the structure of production in the mining sector?
- What are the effects of technical changes on the mining sector output?
Theoretical Background
Various ways of combining factors of production to produce goods and services needed by
the community is described by production function. This function expresses a technical relationship
between inputs and outputs in a simple systematic manner. Production function is a mathematical
equation representing the maximum output or product that a firm or a sector of the economy
canobtain from any fixed and specified series of production inputs on a certain level of technology.
Thus, a production function can be represented as an equation in which the outcomes or the product
is considered as the dependent variable and production inputs as independent variables.
Accordingly, the production function is as follows:
Q  f ( L, K ,...)
(1)
where, the dependent variable (Q) is the output or product and the independent variables are various
production inputs, such as labour (L), capital (K), etc. this function is a neoclassic production
function where L>0 and K>0, defined as a continuous function in which at least two derivation is
possible. Its partial derivatives are shown as below:
Q
 fL
L
Q
 fK
K
 2Q
 f LL
L2
 2Q
 f KK
K 2
(2)
Further, assume that:
fL  0
fK  0
f LL  0
f KK  0
(3)
Not, it is ensured that the final production inputs are positive and decreasing.
In any system of production, there are basically two major and distinct concepts in terms of
efficiency, one is called technical efficiency and the other allocative efficiency (Libenstein, 1988).
In developing equation of production function, it is assumed that engineering and managerial
problems of technical efficiency has been previously solved, so that analysis can focus on the
problems of allocative efficiency. This is why a correct definition refers production function as a
relationship between technical maximum possible yield and the amount of inputs required for
producing this product (Shephard, 1970). Despite this, most theoretic and empirical studies define
the production function carelessly as a technical relationship between product and inputs and the
assumption that such a product is the maximum yield (and minimum inputs) often remains unspoken
(Mishra, 2007).
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Neoclassical total production function is based on features such as final descent productivity
andsubstitutability oflabour and capital together. This function can be obtained with regard to
product per capita and capital per worker, as follows.
Q
K
 A  f ( )  q  A  f (k )
L
L
(4)
Figure 2: neoclassical total production function
As shown in Figure 2, the increase in the capital input moves the curve towards higher
position (more products), while shifting technology from A1 to A2 (assuming A2>A1) will move the
curve upward. This shift means that the same amount of inputachieves more yields. In the
economics literature, it is referred to as technical changes.
Total production function is a relationship that is used to describe the technical relations at
the macro level. Theoretically, this function is the sum of micro production functions. However,
there are piles of works and papers, which were developed from the 1940s onwards, that integrating
micro production functions to a macro production function can be quite difficult and problematic
(Philip & Fisher, 2003). At least, awareness of these problems seems necessary for every economist
who has started practical research. According to Jonathan Temple, every scholar who has decided to
specify or estimate the total production function needs to know the circumstances (Temple,
2007).Sylos Labini believes that: it is worth reminding these critiques and criticisms, because a
significant and growing number of talented young economists do not know or do not take those
criticisms seriously and continues to design and develop various forms of production functions
(Sylos Labini, 1995).
This is called aggregation problem in the economic literature. This is partly due to the
connections and distinctions between micro and macroeconomics. As long as the production
function describes the relationship between yield and inputs of a firm, problems will be more or less
organized and problems will be the least, as much as possible. However, when one attempts to
identify this in an industry, or sector or the economy, it may be a completely different story. An
industry is generally composed of several firms that produce similar products. Of course, each of the
firms uses inputs according to the cost, returns to scale, production technology and market
conditions.
The total production function of an industry is obtained by relating quantities of the used
inputs to total products produced by all firms of that industry. These issues and many other issues
give significance to these problems and problems with the use of these functions. It should be noted
that the progress toward macroeconomic level (sub-sector, sector and the economy) reveals these
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Seyyed Ali Zeytoon Nejad Moosavian
problems (Mishra, 2007). On economics, these problems have been discussed as topics such as
investment disputes and Cambridge-Cambridge discussions1.
Nevertheless, assuming a total production function still allows our model to be highly
predictive and well adapt the total data. As will be discussed below, experience has shown that the
total production functions generally provide a good approximation of the real world. In a study
published on the new growth theories, Jonathan Temple concludes that although the total production
function is the least convincing among all the components and elements of macroeconomics, still it
is considered by many economists as the prerequisite knowledge and understanding of national
income levels and growth rates (Temple, 1998). Therefore, it should be noted that total production
functionscould never be accused of theory-less modelling. According to Jonathan Temple (2007),
critics of the total production function overemphasize the theory. As a result, there are still
compelling reasons for the use of these functions in many areas despite being criticized.
Now a brief introduction to production functions will be presented here. Despite the
challenges and criticisms for reasons which were briefly mentioned, production functions have had a
strong presence in economic studies and they have been widely used in the economic analysis. Here
is a list of names and basic form of these functions.
• Cobb-Douglas production function:
n
Q  A X i i
(5)
i 1
• Production function with constant elasticity of substitution (CES):
n

Q  A  i X i  
 i 1


v

(6)
where it is assumed that:   1
• Translog production function:
n
 0
n
n
v0
ln Q   0    i ln xi  0.5  ij ln xi ln x j
i 1
i 1 j 1
A0
;  ij   ji
(7)
• Transcendental production function:
Q  AK  L eK  L
• Debertin production function:
Q  AK  L eK  L  KL
(8)
(9)
For more information about details and implications of these functions,see Zeytoonnejad
(2005).
In this section, theoretical background of production function in general, and a brief
introduction of Cobb-Douglas production function, CES, Translog, Transcendental and Debertin
specifically were reviewed. Certainly many other mathematical functional forms canexplain
theproduction process in sectors or the whole economy by limiting the real world, and adopting
certain assumptions. To learn about the history of production functions andtheir formation, see
Mishra (2007). Reviewing the history of production functions, he provided a brief description of
1
So-calledCambridge-Cambridge discussion was a theoretical debate during 1950s and 1960s between Joan Robinson
and allies in Cambridge, England with Paul Samuelson and Robert Solow, in Cambridge,America. In other words, the
debate was between Neo-Ricardians (group I) and neoclassic (Group II). Harcourt (1969) presents a full report of what
passed between them and their discussion.
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features and characteristics of other production functions such as the VES, CMS, GPF, LINEX,
multi-output production functions and other production functions.
Empirical Studies
Production functions are of great importance and frequently useddirectly in the technical
conditions of production, and indirectly in other areas of economics, especially productivity in
different economic sectors and levels. Concerning estimation of these functions, several studies have
been conducted in different economic levels. These studies are reviewed as follows.
Agheli-Kohneshahri (2006) estimated the production function of mines. He reviewed the
consolidated data for mining sector in various provinces during 1996-2002. To estimatethe
production functions of mines, he logarithmically explained Cobb-Douglas,Translog and
transcendental production function. Based on production function estimation by Pooled Least
Square (PLS) and Generalized Least Square (GLS), he found that Iranian mines were workintensive and the factor of production function (The total elasticity of production factors) was
greater than 1. This suggests the existence of increasing returns to scale in the mining sector.
Table 1 summarizes the results.
Table 1: summary of empirical studies regarding estimation of production function
Author
Country Time
Level
Data
Inputs
Functions
AgheliCobb-Douglas,
Iran
1996-2002 Mining
Consolidated K,L
Kohneshahri
transcendental
sector
(2006)
and Translog
Nafar (1996)
Iran
1971-1993 Industries Consolidated K,L
Translog
Rezapoor &
Iran
1998-2004 Hospitals Consolidated Doctors,
Cobb-Douglas
Asefnejad (2005)
nurses, beds,
and other staff
Hadian et al
Iran
2000-2005 Hospitals Consolidated Doctors,
Cobb-Douglas
(2007)
nurses, beds,
and other staff
Zeranejad et al
Iran
1979-2002 Firm
Time series K,L
Cobb(2004)
Douglas,Deberti
n and Translog
Lindenberger
German 1960-1989 Servicing Time series K,L,E
Cobb-Douglas
(2003)
y
Antras (2004)
Americ 1998-1948 private
Time series K,L
Cobb-Douglas
a
sector
Xiang (2004)
Canada 1997-1961 Macro
Time series K,L
Cobb-Douglas
Khalil (2004)
Jordan 2002
Industrial Sectional
Translog
K,L,M
manufactu
ring
Bonga-Bonga
South 2002-1972 Macro
Time series K,L
CES
(2005)
Africa
Shankar&Rao
Singapo 2009-1960 Macro
Time series K,L
CES
(2012)
re
Manonmani
India 2010-1991 Textile
Time series K,L
Cobb-Douglas
(2013)
industry
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Seyyed Ali Zeytoon Nejad Moosavian
Estimation results confirmeda different time trend in the technical developments of
production. Thesingle time trend (STT) is a very slow upward trend in improvement of production
technology during the studiedperiod. However, the multiple time trend (MTT) indicated a very
strong reduction in the trend for the year 1971. The results showed diminishing returns to scale in
the industry of Iran.
Lindenberger (2003) estimated the production function for service sector of Germany. Forms
of functions involved in his research include technological parameters, labour, capital and energy.
The results indicate that the time average of production elasticity for capital, labour and energy has
_
_
_
_
_
_
been   0.54 ,   0.31 and   0.21 during 1960-1978 and   0.53 ,   0.26 and   0.21 during 19781989.
Shankar and Rao (2012) estimated the long-term growth rates of Singapore. For this
purpose,they used a CES production function. The results show that the elasticity of substituting
work by capital was 0.6; technical progress in the economy of Singapore was work intensive and
long-term economic growth rate was about 1.8%.
Mining Sector in the Economy
Geological formations of Iran are dominant in the Zagros and Alborz mountains and the
formation of central plateau is affected by tectonics. Location of Iran on Alps-Himalayan belt
provided its rich resources and a huge variety of minerals. There are 62 types of mature minerals in
Iran, which is rare around the world.
With a vast area, various climates, unique geological and geographical locations, Iran has
unique variety of minerals. With more than 55 billion tonnes of confirmed and probable mineral
reserves, Iran is one of the top 12 in the world. Based on 2004 statistics and in terms of weight
metrics, Iran produces 1.24% of the minerals around the world. Figure 3 shows the production of
minerals by the selected countries.
China
Australia
Canada
South Africa
Chile
Brazil
Turkey
Iran
Other Countries
Figure 3: the fraction of total mineral production for different countries in the world
However, the mining sector still does not achieve the fraction it deserves in the economy of
Iran. Its fraction of GDP is less than 1 percent. The average GDP of Iran during 1976-2006 shows
that the average relative fraction of mining sector in GDP has been small (~0.5%),while the fraction
of GNP, based on 2004 statistics in South Africa (7.11%), Australia (6.4%), Denmark (5.4%),
Mexico (4.3%) and Canada (3%), was much higher than this amount(Zeytoonnejad, 2005).
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Although the fraction of value-added GDP of mining sector is small in Iranian economy, it
has an incremental trend during 1976-2006. To investigate this further, see the diagram below.
Figure 4: time trend of value-added GDP for mining sector
As indicated in the figure above, the contribution of mining sector to GDP has experienced
an increasing trendduring1976-2006.
According to the theory of production, the main variables of production are the value-added
(as output), labour and capital stock (as input). In this section, we will examine these variables in the
period 1976-2006. In this context, time-series diagram of these variables is presented as follows.
Figure 5: value-added for mining sector during 1976-2006
Figure 6: employment in mining sector during 1976-2006
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Seyyed Ali Zeytoon Nejad Moosavian
Figure 7: time trend of capital stock in the mining sector during 1976-2006
As the above diagram shows, the value added, employment and capital stock of the mining
sector have experienced nearly an increasing trend in a given period. Now after an overview of the
variables effective on the production process, the table below reports the annual growth rates of
these variables.
Table 2: average annual growth rate of value-added, labour and capital stock in the mining
sector, 1976-2006
variable
the average annual growth rate
Value-added
5.48%
Labor
2.65%
Capital stock
2.21%
The Model and Variables
This section first introduces the collected data; then, it estimates production function of the
mining sector using Cobb-Douglas, transcendental, Debertin and Translog production functions
based on time-series data related to 1976-2006.
Value added is defined as the difference between value of receipts and payments. Value of
receipts is indeed the total value of mineral production, saleable mineral waste, construction and
major repairs of capital assets by employees and other receipts. In contrast, value of payments is the
total value of materials, low-durable tools, consumed fuel, purchased electricity, purchased water
and other payments. In this paper, information of national accounts was used to collect data on the
value added of the mining sector. National accounts are published annually by the Central Bank.
This data was considered as the real value added in fixed prices in 1998.
The capital stock refers to total capital goods, which are measured in a same unit. In mining
sector, capital goods are durable machinery, vehicles, equipment, buildings and facilities
(disregarding the land value), specific road of the mine, software packages. On the other word,
different capital goods are converted to a common unit of measure and are summed together.
Accordingly, a measure of physical capital stock is obtained in the mining sector.
In this study, data related to capital stock of mining sector was extracted from estimations of
the Central Bank for the period 1975-2002. To estimate the last 5years (2003-2007), the estimation
method of Central Bank was used as follows.
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K t  (1   ) K t 1  I t
(10)
Where, Kt, Kt-1 and It are the capital stock in year t, capital stock in year t-1 and investment in
year tin fixed-prices. δ is the depreciation rate which has been considered 4.7% in consistent with
Amini (2006).
By definition, labour refers to all persons employed in the mining sector working inside or
outside the mine full-time or part-time. Employees are divided into production line employees and
administrative, financial and service employees. Productive employees are those involved in the
exploration, extraction, mineral processing and deal directly with extraction and production,
including Simple and skilled workers, technicians, engineers and transportation staff. Financial,
administrative and servicing Personnel include office, administrative, financial and services staff
and central office who are not directly involved in the extraction and production.
To collect data on labour, this study used Mines Annual Report, which is published annually
by the Statistical Centre of Iran. Although, for this purpose, it was possible to use estimates by the
Central Bank, Macroeconomics Office and the Office of Planning and Budget Organization and the
various reliable studies, data from the Annual Census of Mines was used because of more credibility
of Census data than estimated data.
Unfortunately, there was a gap in the data provided by the Statistical Centre of Iran on the
labour employed in the mining sector for years1977-1984, 1991 and 2005. To obtain the data for
these years, interpolation methods were used. In this respect, the data available for the years before
and after the gap was used as a benchmark. There are basically two types of interpolation method,
exogenous and endogenous. In this study, the exogenous interpolation method was used to address
data gaps.
The exogenous approach assumes the average annual employment growth rate as constant
and estimates the employment rate regardless of changes in variables effective on employment, such
as investment and production. Let m represent the average annual employment growth rate in two
consecutive periods when census has been carried out; employment rate in year t is obtained as
follows:
Lt  (1  m) t
(11)
Similarly, few data gaps in the time series of census employment by the Statistics Centre of
Iran mines were eliminated.
Therefore, the used variables and data sources are listed as follows.
Table 3: data resources and definition of the used variables
Resource
Definition
Central Bank
Value-added (production)
Statistical Center of Iran
Employment
Central Bank
Capital stock
Variable
Q
L
K
As noted earlier, many mathematical functional forms are able to explain production process
in economic sectors by limiting the real world and adopting some assumptions. In order to estimate
the production function in the mining sector, four different types of production function, i.e. CobbDouglas, transcendental, Debertin and Translog as specified below:
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Seyyed Ali Zeytoon Nejad Moosavian
Table 4: summary of explained models for estimation
Production function
Explained model
ln Q     ln K   ln L
unconstrainedCobb-Douglas (C-D)
lnQ     ln K   ln L  T
Unconstrained Tinbergen C-D
Q
K
Constrained arbitrary C-D
ln( )  ln A    ln( )
L
Constrained Tinbergen arbitrary C-D
Transcendental
Debertin
Translog
L
Q
K
ln( )  ln A    ln( )  T
L
L
lnQ    1L  2 lnL 1K 2 lnK
ln Q     1 ln L   1 ln K   2 L   2 K  KL
lnQ    1 ln L  2 (lnL)2  1 ln K  2 (lnK)2   (lnL)(lnK)
In the explained production functions, coefficients of the variable trend are considered as a
cause of technical changes and a positive sign of the coefficients indicates the technical progress.
Cobb-Douglas model can be estimated under several scenarios. This function is estimated in
constrained and unconstrained as well as simple and Tinbergen forms.
Experimental Results
Among above models, the results of some models were not consistent with theories of
economics; therefore, those results were avoided to report. In most of these models, large number of
explanatory variables reduces the degrees of freedom and causes non-compliance with the principle
of scarcity (saving) followed by some problems; on the other hand, repeating variables in different
ways causes co-linearity problems for the model and influences the standard deviation and statistical
significance of the variables. It is noteworthy that the variable virtual war was also inserted in the
models and it was found that it was not significant in any of the above models.
In this study, the unconstrained Tinbergen Cobb-Douglas model provided the best results in
compliance with theories of the economics and in consistent with statistic and economic measures.
Before estimation, the first step is to test the reliability of variables. Then, the production function of
mining sector is estimated. Next, the assumptions and requirements are evaluated by proper tests.
Reliability
The economic analysis assumes that there is a long-term balanced relationship between
variables considered in an economic theory. In practical econometric analysis to estimate long-run
relationships between variables, the mean and variance are constant over time and independent of
the time factor. Therefore, a behavioural consistency is implicitly assumed for them. However,
research has found that the behavioural consistency of the time series variables is not fulfilled in
most cases.
Therefore, the classic t and F tests of estimation methods, in which behavioral consistency or
the so-called reliability of variables is not fulfilled, are not validated and the results will be
misleading. This problem is referred to as fake regression. Consequently, variables need to be tested
for reliability in order to ensure the results.
A time series variable is reliable when the mean, variance and autocorrelation coefficients
remain constant over time. In other words, if starting time of a series changesand mean and
variance-covariance remain unchanged, the series will be reliable. A graph of logarithmic timeseries variables used in this study is presented below.
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Figure 8: the logarithmic values of the time series variables used in the models
Figure (8) implicitly suggests a time trend and that above variables follow the time factor. In
other words, this graph implicitly indicates unit roots in the variables above. To test this, we used
the following tests, in order to be explicit about the reliability of the above variable.
Unit root tests such as Augmented Dickey-Fuller (ADF) and Philips-Perron (PP) were used
2
. Summary of results is presented in Table
for this. The results show that variables are all
(5).
Table 5: summary of results from reliability tests conducted for logarithm of variables
Variable ADF level PP level First order difference First order difference
Result
of ADF
of PP
LL
-2.157
-2.071
-6.257
-10.904
LK
-2.751
-2.472
-4.124
-4.114
LQ
-1.120
-1.120
-4.979
-4.984
While testing levels, the critical values at 1%, 5% and 10% were -4.297, -3.568 and -3.218,
respectively; for the first order difference, the critical values at 1 %, 5% and 10% were -4.310, 3.574 and -3.222, respectively.
Now, the production function is estimated using the ordinary least squares estimator. In
general, these estimators as Gauss-Markov theorem are the best linear unbiased estimators (BLUE).
However, this method can be used to estimate the coefficients when the model satisfies the
following assumptions:
- Lack of bias ( E (u i )  0 )
- Lack of variance anisotropy ( E (ui2 )   2 I )
- Lack of autocorrelation of disturbing elements ( E (ui , u j )  0 in i  j
- Lack of correlation between disturbing elements and explanatory variables ( E ( X i u i )  0 )
- Normal distribution of disturbing elements with variance  u2 and the expected value of zero
(u~Nσ2))
In estimating the production function of mining sector, the best model based on theoretic
econometrics is the unconstrained Tinbergen Cobb-Douglas production function. Considering the
conditions above, we have attempted to estimate this function. Table 6 summarizes the results of the
estimation of the production function:
2
However, the same tests of the reliability were conducted on logarithmic values of capital and value added per capita;
the results of both tests showed the reliability was I(1) for both variables.
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Seyyed Ali Zeytoon Nejad Moosavian
Table 6: summary of results from estimation of unconstrained production function for mining
sector
Parameters, measures, statistics
Values
Elasticity of production to capital) α(
0.44
1.88
t-Statistic ofߙ
Elasticity of production to labor (β)
0.41
1.47
t-Statistic of ߚ
Factor of technical change
0.08
1.67
t-Statistic related to factor of technical change
The coefficient of AR (1)
0.9
10.58
t-Statistic related to coefficient of AR (1)
2
98%
R
2
97%
R
F-Statistic
Durbin-Watson
Number of observations (n) after adjustment
255
1.93
30
The results from this estimation show that elasticity of production to capital and labour was
0.44 and 0.41, respectively. The factor of technical changes was positive and significant in the
model, which means the positive impact of technological change on output of the mining sector. To
solve the problem of autocorrelation in the model, the component AR(1) was added to the model. In
these circumstances, the Durbin-Watson (DW) approached the number 2suggesting no
autocorrelation between disturbing elements. The coefficient of determination and the adjusted
coefficient of determination were 98% and 97%, respectively, indicating the good explainability of
the model. In other words, the coefficient R2=985 indicates that 98% of variation in the dependent
variable (value-added) can be explained by the explanatory variables. Significance of coefficients (t)
was also good, so that coefficients of capital (95% confidence) and coefficients of labour and time
trend (90% confidence) were significant. Numerical value of f-statistic indicates the significance of
the model as a whole.
To see the actual graph of value-added and the fitted line (estimated regression line) as well
as the plot of error terms, refer to. Partial compliance and proper fitness of the regression line on the
graph of value-added indicate the suitability of the specified model and ability of the estimated
relationship in economic forecasts.
Figure 9: fitness of the estimated unconstrained production function on the graph of valueadded with the graph of disturbing elements
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Thus, indices of the estimated model are acceptable according to statistical, theoretical and
econometric criteria; therefore, the estimated model can be accepted as a schema. Now, the schema
is evaluated for classical assumptions such as variance anisotropy, normality, etc. The degree of
reliability and validity of the model will be determined accordingly.
Anisotropy Analysis of Variance
One of the classic assumptions is equal variances of the disturbing elements in different
periods. In other words, E (u i2 )   2 I where i  1,2,000, n . Violation of this assumption creates a
problem called variance anisotropy. By testing variance anisotropy of regression through BreuschPagan-Godfrey method, it was determined that the assumption of variance anisotropy could be
rejected. Therefore, there is no problem of variance anisotropy in the estimated model.
Autocorrelation test
To investigate the problem of autocorrelation, Breusch-Godfrey test (LM test) was used. The
results of this test for the primary unconstrained model (before insertingAR(1)), implies the problem
of autocorrelation in the estimated model. The diagram of autocorrelation and partial correlation of
the disturbing elements is presented as follows.
Figure 10: the autocorrelation and partial correlation of disturbing elements in the primary
unconstrained model
Autocorrelation problem is clearly visible in the graphs above. In order to solve this problem,
an AR(1) was added to the model, and thus the problem was resolved. Results of Breusch-Godfrey
test, after inserting AR(1) into the model, suggest that the problem was resolved. Accordingly, the
diagram of autocorrelation is presented as follows.
Figure 11: autocorrelation and partial correlation of disturbing elements in the final
unconstrained model
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Seyyed Ali Zeytoon Nejad Moosavian
Therefore, adding the component AR(1) to the model resolved the autocorrelation problem.
We will continue to investigate other assumptions of the classical regression model.
Normality of the disturbing elements
The results showed that disrupting elements were distributed normally. To explore this, see
the diagram (12).
Figure 12: the results obtained from the statistical distribution of disturbing elements in the
unconstrained model
Thus, Figure 12 shows that the assumption of normal distribution for the random process of
disturbing element is true; in other words, u ~ N (0,  2 ) . This in turn suggests E (u i )  0 which
indicates that another classical assumption is also true. Calculation of E (u i ) shows that its value is 1/85186E-12 which is almost equal to zero.
Independence of disrupting elements from the explanatory variables
Results from calculating the coefficient of correlation between disturbing elements and
explanatory variables of capital stock and labour were 0.054 and -0.098, respectively, which suggest
the independence of disturbing elements from both explanatory variables in the estimated model.
Thus, the assumption of independence of disrupting elements from the explanatory variable is true.
Therefore, it was determined that all the classical assumptions are true in the estimated model and
there is no violation of the classical assumptions.
Co-linearity
Co-linearity originally means a linear relationship and strong correlation between the
explanatory variables of the regression model. Even if the co-linearity is too severe, OLS estimators
maintain the BLUE feature. Some researchers fear that the explanatory variables are co-linear, but
co-linearity does not violate any of the assumptions of regression. Unbiased and consistent
estimators and their errors are correctly estimated. The only effect of co-linearity is that estimations
of the coefficients are obtained with large standard errors. As this effect is observed for the
independent variables with small variances, this is also true for small number of observations.
Empirical rules based on which the presence or absence of co-linearity can be determined are as
follows:
- The high R 2 and the low number of significant t ratios
- High paired correlation between the explanatory variables
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Review of the empirical regularities found no severe co-linearity in the model.
Now as the final stage of co-integration, it is necessary to calculate the time series of disturbing
elements and test the reliability of this series. Series of the disturbing elements was obtained using
outputs ofEviws6 software. As the last step of co-integration, the time series of disturbing elements
is examined for reliability. Only if the time series is reliable, the results of ordinary least squares
estimation are validated. Using both ADF and PP tests, reliability of the series was investigated.
Summary of the results is listed in Table 7.
Table 7: summary of results from reliability tests for disturbing elements of the unconstrained
model
Variable
ADF level
PP level
Result
Disturbing elements
-5.096
-5.093
The results from both methods suggest that the series is reliable. Thus, the estimated model is
acceptable as a schema.
Conclusion
Despite the low contribution of mining sector to GDP, its effect is considerable on the
secondary production of wealth. High diversity and abundance of mineral wealth in the Iranian
economy has created a considerable potential. The mining sector, as the main source of primary
materials needed for important industries and besides employment and balanced regional economic
development, is of great importance. However, the economic exploitation of these exhaustible
resources is possible by optimal composition of the primary factors of production, namely labour,
machinery, intermediate goods and energy.
By reviewing theoretical background, empirical literature and status of the mining sector in
the Iranian economy, this study estimated the production function of mining sector and revealed the
mediatory structure of production in mines of Iran. In other words, the structure of Iranian mining
sector is work-intensive and capital-intensive. This is because of the fact that elasticity of production
to capital and labour has been 0.44 and 0.41, respectively, which are not considerably different. On
the other hand, the production is in economic zone to both inputs. The factor of function has been
0.85 for this sector, indicating the decreasing return to scale. Moreover, the coefficient of trend, as
the index of technical changes in production, was significant, suggesting the positive effect of
technical changes on output of the mining sector.
Therefore, to promote level of technology, to create stability in order to provide a bed for
investment, to develop infrastructures, to make policies to increase incentives, to increase R & D, to
revise scales of production3 in order to use economies of scale and spread of information banks of
Geology and exploration can be helpful in the efficiency of this sector.
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3
According to economic theory, the optimal scale of production isa level of production in which the average cost (AC)
of production is minimal.
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Seyyed Ali Zeytoon Nejad Moosavian
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